Orthogonal Frequency Division Multiplexing - OFDM

Multipath Radio Channel

Frequency-Selective Radio Channel

-10

-5

0

5

10

15

20

Frequency

Power response [dB]

Concept of parallel transmission

Channel impulse response

1 Channel (serial)

2 Channels

8 Channels

Time

In practice: 50 … 8000

Channels (sub-carriers)

Channels are transmitted at different frequencies (sub-carriers)

Concept of parallel transmission

Channel impulse

response

1 Channel (serial)

Channel

transfer function

Channels are

“narrowband”

2 ChannelsFrequency

Frequency

8 ChannelsFrequency

FrequencyTime

Signal is

“broadband”

5

Impact of fading

f

f

t

t

t

t

t

h(t)

s(t)

s(t)

S(f)

S(f)

r(t)

r(t)

High bit rate

Low bit rate

H(f)

f

6

p4(t)

Frequency Selective fading

�flat fading

t

t

t

th(t)

s(t)

p1(t)

r(t)

H(f)

f

p2(t)

t

p3(t)

p4(t)

p3(t)

Concept of an OFDM signal

Ch.1

Ch.2 Ch.3 Ch.4 Ch.5 Ch.6 Ch.7 Ch.8 Ch.9 Ch.10

Saving of bandwidth

Ch.3 Ch.5 Ch.7 Ch.9Ch.2 Ch.4 Ch.6 Ch.8 Ch.10

Ch.1

Conventional multicarrier techniques

Orthogonal multicarrier techniques

50% bandwidth saving

frequency

frequency

8

OFDM DEFINITION

� OFDM = Orthogonal FDM

� Carrier centers are put on orthogonal frequencies

� ORTHOGONALITY - The peak of each signal coincides with zero crossing of other signals

� Subcarriers are spaced by 1/ Ts

9

Orthogonal Subcarriers

10

A simplified view

S-P

Cos 2πf1t

Cos 2πf8t

+Input bitsInput bitsInput bitsInput bits

s(t)

P-S

Cos 2πf1t

Cos 2πf8t

r(t) Rep Output Output Output Output

bitsbitsbitsbits

11

Alternate View

12

OFDM Theory

13

Discrete Time Equivalent

� Inverse Discrete Fourier Transform �

s(n) = ∑ dk exp( j 2π k n/N)

� N-point IDFT � N2 complex multiplications

� Inverse Fast Fourier Transform

� Radix 2 N-point IFFT � (N/2). log2 N

� Radix 4 N-point IFFT � (3/8). N. ( log 2 N - 2)

N -1

k=0

14

15

Complexity of OFDM versus Single Carrier

� Key difference between OFDM and single carrier transmission is FFT versus equalizer

� Complexity of 64 point radix-4 FFT in IEEE 802.11a OFDM=96 million multiplications per second

� 16 taps OQPSK or GMSK Equalizer for same data rates above needs 768 million multiplications per second

� OFDM order of magnitude less complex

16

Cyclic Prefix

17

Generation of ICI

18

Cyclic Extension

19

Cyclic Prefix

20

Cyclic Extension

21

Windowing

22

Cyclic Extension & Windowing(filtering ?)

23

OFDM ADVANTAGES

� OFDM is spectrally efficient � Orthogonality & IFFT/FFT operation ensures that sub-carriers

do not interfere with each other.

� OFDM has an inherent robustness against narrowband interference.� Narrowband interference will affect at most a couple

of subchannels.� Information from the affected subchannels can be

erased and recovered via the forward error correction (FEC) codes.

� Equalization is very simple compared to Single-Carrier systems

24

OFDM ADVANTAGES

� OFDM has excellent robustness in multi-path environments.� Cyclic prefix preserves orthogonality between sub-

carriers.� Cyclic prefix allows the receiver to capture multi-

path energy more efficiently.

� Ability to comply with world-wide regulations:� Bands and tones can be dynamically turned on/off

to comply with changing regulations.

� Coexistence with current and future systems:� Bands and tones can be dynamically turned on/off

for enhanced coexistence with the other devices.

25

OFDM DRAWBACKS

� High sensitivity inter-channel interference, ICI

� OFDM is sensitive to frequency, clock and phase offset

� The OFDM time-domain signal has a relatively large peak-to-average power ratio

� tends to reduce the power efficiency of the RF amplifier

� non-linear amplification destroys the orthogonality of the OFDM signal and introduces out-of-band radiation

26

OFFSET ESTIMATION & SYNCHRONIZATION

27

OFDM Preamble

28

OFDM Transceiver

CodingCodingCodingCoding

Binary

Input

Data InterleavingInterleavingInterleavingInterleaving

QAM QAM QAM QAM

mappingmappingmappingmapping

PilotPilotPilotPilot

InsertionInsertionInsertionInsertionS S S S ---- PPPP

IFFTIFFTIFFTIFFT

FFTFFTFFTFFT

DecodingDecodingDecodingDecoding DeDeDeDe----InterleavingInterleavingInterleavingInterleavingQAM QAM QAM QAM

demappingdemappingdemappingdemapping

Channel Channel Channel Channel

CorrectionCorrectionCorrectionCorrectionP P P P ---- SSSS

Binary

Output

Data

S S S S ---- PPPP

P P P P ---- SSSS

Add Cyclic Add Cyclic Add Cyclic Add Cyclic

extension extension extension extension

& Windowing& Windowing& Windowing& Windowing

DACDACDACDACRF RF RF RF TxTxTxTx

Remove Remove Remove Remove

Cyclic Cyclic Cyclic Cyclic

extension extension extension extension

Timing &Timing &Timing &Timing &

Freq.Freq.Freq.Freq.

Sync.Sync.Sync.Sync.

ADCADCADCADCRF RxRF RxRF RxRF Rx

29

Selection of OFDM parameters

� Bandwidth, bit rate, delay spreadBandwidth, bit rate, delay spreadBandwidth, bit rate, delay spreadBandwidth, bit rate, delay spread

� Guard time Guard time Guard time Guard time TTTTgggg

� 2 to 4 times delay spread 2 to 4 times delay spread 2 to 4 times delay spread 2 to 4 times delay spread ���� 2222σσσσ to to to to 4444σσσσ

� depends on the order of modulation employeddepends on the order of modulation employeddepends on the order of modulation employeddepends on the order of modulation employed

� Symbol duration > Guard time to maximize SNRSymbol duration > Guard time to maximize SNRSymbol duration > Guard time to maximize SNRSymbol duration > Guard time to maximize SNR� More More More More subcarrierssubcarrierssubcarrierssubcarriers, smaller spacing, implementation complexity, more sensitivity , smaller spacing, implementation complexity, more sensitivity , smaller spacing, implementation complexity, more sensitivity , smaller spacing, implementation complexity, more sensitivity

to phase noise & frequency offset, high PAPRto phase noise & frequency offset, high PAPRto phase noise & frequency offset, high PAPRto phase noise & frequency offset, high PAPR

� Symbol duration Symbol duration Symbol duration Symbol duration ���� 5 x Guard time ( 15 x Guard time ( 15 x Guard time ( 15 x Guard time ( 1----dB SNR loss )dB SNR loss )dB SNR loss )dB SNR loss )

� TTTTFFTFFTFFTFFT = 5 x = 5 x = 5 x = 5 x TTTTgggg ���� TTTTofdmofdmofdmofdm = T= T= T= TFFT FFT FFT FFT + + + + TTTTgggg

� SubcarrierSubcarrierSubcarrierSubcarrier spacing spacing spacing spacing ∆∆∆∆f = 1 / Tf = 1 / Tf = 1 / Tf = 1 / TFFTFFTFFTFFT

� Number of Number of Number of Number of subcarrierssubcarrierssubcarrierssubcarriers = 3= 3= 3= 3----dB BW / dB BW / dB BW / dB BW / ∆∆∆∆f f f f

30

Example :� Bit rate = 20 MbpsBit rate = 20 MbpsBit rate = 20 MbpsBit rate = 20 Mbps

� Tolerable delay spread = 200 nsTolerable delay spread = 200 nsTolerable delay spread = 200 nsTolerable delay spread = 200 ns

� Bandwidth < 15 MHzBandwidth < 15 MHzBandwidth < 15 MHzBandwidth < 15 MHz� Tg = 800 ns

� Tofdm = 5 x Tg + Tg = 4.8 µµµµsec

� ∆∆∆∆f = 1 / 4 µµµµsec = 250 KHz

� Number of bits in one OFDM symbol = 20 Mbps x 4.8 µµµµsec = 96

� 16-QAM with rate ½ Conv. Coding ���� 2 bits / symbol / subcarrier ���� 48 subcarriers ���� 48 x 250 KHz = 12 MHz < 15 MHz

� QPSK with rate ¾ coding ���� 1.5 bits / symbol / subcarrier ���� 64 subcarriers

���� 64 x 250 KHz ���� 16 MHz > 15 MHz

� 64 point IFFT / FFT ���� 16 zero subcarriers ���� oversampling

Given requirements

31

OFDM based ApplicationsOFDM based ApplicationsOFDM based ApplicationsOFDM based Applications

� DABDABDABDAB----OFDM OFDM OFDM OFDM ���� Digital Audio BroadcastingDigital Audio BroadcastingDigital Audio BroadcastingDigital Audio Broadcasting

� DVDDVDDVDDVD----OFDM OFDM OFDM OFDM ���� Digital Video Broadcasting Digital Video Broadcasting Digital Video Broadcasting Digital Video Broadcasting

� ADSLADSLADSLADSL----OFDM OFDM OFDM OFDM ���� Asynchronous Digital Subscriber LineAsynchronous Digital Subscriber LineAsynchronous Digital Subscriber LineAsynchronous Digital Subscriber Line� Wireless Local Area NetworkWireless Local Area NetworkWireless Local Area NetworkWireless Local Area Network

� IEEEIEEEIEEEIEEE----802.11a, IEEE802.11a, IEEE802.11a, IEEE802.11a, IEEE----802.11g, .11n802.11g, .11n802.11g, .11n802.11g, .11n

� ETSI BRAN (Hyperlan/2)ETSI BRAN (Hyperlan/2)ETSI BRAN (Hyperlan/2)ETSI BRAN (Hyperlan/2)

� Wireless MAN 802.16 Working Group of IEEEWireless MAN 802.16 Working Group of IEEEWireless MAN 802.16 Working Group of IEEEWireless MAN 802.16 Working Group of IEEE

� 802.16 a, b 802.16 a, b 802.16 a, b 802.16 a, b -------- 2 to 11 GHz2 to 11 GHz2 to 11 GHz2 to 11 GHz

� Mobile Mobile Mobile Mobile WiMAXWiMAXWiMAXWiMAX

32

OFDM Systems

0.64-8.192231.91.1041.1044.312536-127

7-28

256 (down)

64 (up)

ADSL

3.07224/48/96

msec

2.0481.5361.0015362048

8192

DAB

0.68-14.922249.1747.6434.4641712

842

2048

1024

DVB-T

6-543.2

0.8

20 16.56 312.5 52

4

64802.11a

6-543.2

0.8

2016.25312.552

4

64HyperLAN/2

Data

Rate

Mbits/s

Symbol

Duration

µµµµsec

Sample

Rate

MHz

Bandwidth

MHz

Channel

Spacing

kHz

Number

Carriers

Transform

Size

System

33

Create Multiple Channel

FDM

POTSPOTS

UpstreamUpstream

DownstreamDownstream

Echo Cancellation

FrequencyFrequency

1 Mhz1 Mhz

ADSL

Thank You